... or a George Box (I believe) said: The crucial "Declaration of Independence."
Bert Gunter "The trouble with having an open mind is that people keep coming along and sticking things into it." -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip ) On Sat, Mar 20, 2021 at 4:25 PM John Maindonald <john.maindon...@anu.edu.au> wrote: > No, it is not distribution free. Independent random sampling is assumed. > That is a non-trivial assumption, and one that is very often not true or > not > strictly true. > > > John Maindonald email: john.maindon...@anu.edu.au<mailto: > john.maindon...@anu.edu.au> > > > On 21/03/2021, at 00:00, r-help-requ...@r-project.org<mailto: > r-help-requ...@r-project.org> wrote: > > From: Jiefei Wang <szwj...@gmail.com<mailto:szwj...@gmail.com>> > Subject: Re: [R] about a p-value < 2.2e-16 > Date: 20 March 2021 at 04:41:33 NZDT > To: Spencer Graves <spencer.gra...@effectivedefense.org<mailto: > spencer.gra...@effectivedefense.org>> > Cc: Bogdan Tanasa <tan...@gmail.com<mailto:tan...@gmail.com>>, Vivek Das < > vd4mm...@gmail.com<mailto:vd4mm...@gmail.com>>, r-help < > r-help@r-project.org<mailto:r-help@r-project.org>> > > > Hi Spencer, > > Thanks for your test results, I do not know the answer as I haven't > used wilcox.test for many years. I do not know if it is possible to compute > the exact distribution of the Wilcoxon rank sum statistic, but I think it > is very likely, as the document of `Wilcoxon` says: > > This distribution is obtained as follows. Let x and y be two random, > independent samples of size m and n. Then the Wilcoxon rank sum statistic > is the number of all pairs (x[i], y[j]) for which y[j] is not greater than > x[i]. This statistic takes values between 0 and m * n, and its mean and > variance are m * n / 2 and m * n * (m + n + 1) / 12, respectively. > > As a nice feature of the non-parametric statistic, it is usually > distribution-free so you can pick any distribution you like to compute the > same statistic. I wonder if this is the case, but I might be wrong. > > Cheers, > Jiefei > > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.